Estimation of soil hydraulic parameters by fractal geometry and the solution of the Richards equation

Abstract

Two constraints prevent widespread adoption and application of mechanistic models for predicting solute and water transport in soils and aquifers. They are (a) the high cost and technical difficulty of measuring the transport coefficients required to operate the models, and (b) the high spatial variability of the transport coefficients. The purpose of this research is to develop indirect methods for estimating the input data of model from readily available soil characterization data. Two hypotheses of this approach are (a) soil particle size distribution, water retention curves Φ(θ) and hydraulic conductivity curves K(θ) obey the fractal model, and (b) the fractal dimensions of the water retention curve and hydraulic conductivity curve are related to the fractal dimension of the soil particle size distribution. Four types of fractal models for particle size distribution were developed. Published datasets of coal, limestone, phosphate rock, and soil particle size distribution 10 soil series from the Southern Region of the United States were used as a data source for testing the model. The results show that the majority of samples obey the fractal power law. Datasets of water retention curves of over 3000 samples from the same source were analyzed by the fractal model. The majority of the fractal dimensions ranged from 2.0 for sandy soils to 2.9 for clayey soils. A significant linear relationship between the fractal dimensions of soil particle size distribution and water retention curve was found, enabling the water retention curves to be estimated from particle size distribution data. Because of the technical difficulty in measuring the K(θ) and therefore the inadequacy of a reliable data base, it was not possible to test the predicted relationship between Φ(θ) and K(θ). To circumvent this problem, an analytical solution to the Richards equation was developed. This method enables D(θ) to be derived from a simple determination of the position of the wetting front. Finally, scaling theory was utilized to enable the numerical solution of the Richards equation for one soil to be applied to other soils.